OP wanted a good AP Morde build, not to be told why he's useless. What's worked well for me as DPS/Off-Tank Morde is the following:
Boots of Swiftness - Key because he's a slow piece of metal with no slow/stun/disable. Although I would argue that the new CDR boots would be better, haven't tried them out yet though.
Rylai's Crystal Scepter - Gives him massive AOE slows, and you can use your Ult to DOT someone and keep up with them ensuring they DIE and you get the ghost.
Abyssal Scepter - Seems kinda silly getting 2 scepters, but then again, the MR gained and MR lost by the opponents makes you deal actual damage with your abilities and helps your teams casters.
Deathcap - You could get this first, but I find that having AOE slows helps me get more kills than the additional AP would early, and when you complete it you get a huge Spike in damage.
Sunfire Cape - Your last tanky type item, with constant AOE slows, and huge shield tanking powers, you now have enough armor/MR and HP to just walk into battles and AOE the snot out of the team, not dying and dealing a lot of damage via Sunfire/Creeping Death/Ult/Siphon/Mace of Spades.
While most builds tell you to focus on Armor/MR instead of HP, and this is usually true with Morde, I find that when going AP, all the items you want anyway have these built in. So you can get the best of all the worlds. You get a decently high AP, you get surviveability with increasing your shield generation by reducing their MR, and increasing your AP. You get higher DPS output with AP than you do by simply being able to stand around and fire off another weak spell. You cause massive chaos when slowing the entire enemy team with Mace/Siphon and Creeping Death just chasing people with Sunfire while they take Creeping Death dmg, and being slowed.
I like this build because I feel it's more the feel of Mordekaiser. I would think that a champion like him would walk around the battlefield and that no one would want to be near him, always trying to run away while he tanks and deals large sums of AOE dmg.